simulate interaction of fluids with different viscosity
Disclaimer : I'm afraid I've not done much beyond scripting meshes at this point. I did once play with particle emitters and some constraint stuff hence this suggestion but this is a bit of a hack and may cost you more time then save you any.

Based off of the video you could try the following :

Setup a plane or may be even a cube with the top face removed. Using a particle emitter you could fill this cube at various locations to 'add ink' as it were. The tricky thing is then to make the particles emitted in a single addition cling to one another but repulsive to any prior and/or successive addition. That is for a single emission you want those particles to group in some way, perhaps there is some sort of elastic constraint you could apply. Then for separate emissions you basically want each addition to repel one another slightly.

You may have to make all emissions adhere to the bin/plate though, this is most easily by just doing things in the vertical direction.